91. Reversible complement cyclic codes over finite chain ringsMonika Dalal, Sucheta Dutt, Ranjeet Sehmi, 2026, izvirni znanstveni članek Opis: In this paper, necessary and sufficient conditions for the reversibility of a cyclic code of arbitrary length over a finite commutative chain ring have been derived. MDS reversible cyclic codes having length ps over a finite chain ring with nilpotency index 2 have been characterized and a few examples of MDS reversible cyclic codes have been presented. Further, it is shown that the torsion codes of a reversible cyclic code over a finite chain ring are reversible. Also, an example of a non-reversible cyclic code for which all its torsion codes are reversible has been presented to show that the converse of this statement is not true. The cardinality and Hamming distance of a cyclic code over a finite commutative chain ring have also been determined.
Ključne besede: cyclic codes, reversible codes, torsion codes, generators
Objavljeno v RUP: 22.12.2025; Ogledov: 139; Prenosov: 1
 Celotno besedilo (445,36 KB) |
92. Clar and Fries structures for fullerenesPatrick W. Fowler, Wendy Myrvold, Rebecca L. Vandenberg, Elizabeth J. Hartung, Jack E. Graver, 2026, izvirni znanstveni članek Opis: Fries and Clar numbers are qualitative indicators of stability in conjugated π systems. For a given Kekulé structure, call any hexagon that contains three double bonds benzenoid. The Fries number is the maximum number of benzenoid hexagons, whereas the Clar number is the maximum number of independent benzenoid hexagons, in each case taken over all Kekulé structures. A Kekulé structure that realises the Fries (Clar) number is a Fries (Clar) structure. For benzenoids, it is not known whether every Fries structure is also a Clar structure. For fullerenes C_n, it is known that some Clar structures in large examples correspond to no Fries structure. We show that Fries structures that are not Clar occur early: examples where some Fries structure is not Clar start at C_34, and examples where no Fries structure is Clar start at C_48. Hence, it is unsafe to use fullerene Fries structures as routes to Clar number. However, Fries structures often describe the neutral fullerene better than a Clar structure, e.g. in rationalising bond lengths in the experimental isomer of C_60. Conversely, an extension of Clar sextet theory suggests the notion of anionic Clar number for fullerene anions, where both pentagons and hexagons may support sextets.
Ključne besede: chemical graph theory, fullerenes, benzenoids, Clar, Fries, Kekule, perfect matching
Objavljeno v RUP: 22.12.2025; Ogledov: 142; Prenosov: 1
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93. Platonic configurations of points and linesJurij Kovič, Aleksander Simonič, 2026, izvirni znanstveni članek Opis: We present some methods for constructing connected spatial geometric configurations (p_q, n_k) of points and lines, preserved by the same isometries of Euclidean space E³ as the predetermined Platonic solid. In this paper, we are mainly interested in configurations (n₃), (n₄), and (n₅), but also in unbalanced configurations (p₃, n₄), (p₃, n₅), and (p₄, n₅).
Ključne besede: configuration of points and lines, symmetry group, Platonic solid, centrally symmetric solid, projection from a point
Objavljeno v RUP: 22.12.2025; Ogledov: 123; Prenosov: 1
Celotno besedilo (533,56 KB) |
94. Numerical semigroups with distances no admisible between gaps greater than its multiplicityJ. C. Rosales, Manuel B. Branco, Márcio A. Traesel, 2025, izvirni znanstveni članek Opis: Let A pabe a nonempty subset of positive integers. In this paper we study the set of numerical semigroups that fulfill: if {x,y} ⊆ ℕ\S and x > y > min(S\{0}), then x-y ∉ A.
Ključne besede: Frobenius pseudo-varieties, genus number, numerical semigroups, PD(A)-semigroup and tree (associated to a PD(A)-semigroup)
Objavljeno v RUP: 21.12.2025; Ogledov: 179; Prenosov: 1
Celotno besedilo (356,42 KB) |
95. On the leaves of graph search treesRobert Scheffler, 2026, izvirni znanstveni članek Opis: Graph searches and their respective search trees are widely used in algorithmic graph theory. The problem whether a given spanning tree can be a graph search tree has been considered for different searches, graph classes and search tree paradigms. Similarly, the question whether a particular vertex can be visited last by some search has been studied extensively in recent years. We combine these two problems by considering the question whether a vertex can be a leaf of a graph search tree. We show that for particular search trees, including DFS trees, this problem is easy if we allow the leaf to be the first vertex of the search ordering. We contrast this result by showing that the problem becomes hard for many searches, including DFS and BFS, if we forbid the leaf to be the first vertex. Additionally, we present several structural and algorithmic results for search tree leaves of chordal graphs.
Ključne besede: graph search, graph search trees, leaves, chordal graphs
Objavljeno v RUP: 21.12.2025; Ogledov: 172; Prenosov: 1
Celotno besedilo (515,71 KB) |
96. Tight upper bounds for the p-anionic Clar number of fullerenesAaron Slobodin, Wendy Myrvold, Gary MacGillivray, Patrick W. Fowler, 2026, izvirni znanstveni članek Opis: A fullerene is an all-carbon molecule with a polyhedral structure where each atom is bonded to three other atoms and each face is either a pentagon or a hexagon. Fullerenes correspond to 3-regular planar graphs whose faces have sizes 5 or 6. The p-anionic Clar number C_(p)(G) of a fullerene G is equal to p + h, where h is maximized over all choices of p + h independent faces (exactly p pentagons and h hexagons) the deletion of whose vertices leave a graph with a perfect matching. This definition is motivated by the chemical observation that pentagonal rings can accommodate an extra electron, so that the pentagons of a
fullerene with charge −p, compete with the hexagons to host ‘Clar sextets’ of six electrons, and pentagons will preferentially acquire the p excess electrons of the anion.
Tight upper bounds are established for the p-anionic Clar number of fullerenes for p > 0. The upper bounds are derived via graph theoretic arguments and new results on minimal cyclic-k-edge cutsets in IPR fullerenes (fullerenes that have all pentagons pairwise disjoint). These bounds are shown to be tight by infinite families of fullerenes that achieve them.
Ključne besede: chemical graph theory, anionic Clar number, fullerenes
Objavljeno v RUP: 21.12.2025; Ogledov: 182; Prenosov: 1
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97. On the main distance-based entropies: the eccentricity- and Wiener-entropyStijn Cambie, Yanni Dong, 2026, izvirni znanstveni članek Opis: We define the Wiener-entropy, which is together with the eccentricity-entropy one of the most natural distance-based graph entropies. By deriving the (asymptotic) extremal behaviour, we conclude that the Wiener-entropy of graphs of a given order is more spread than is the case for the eccentricity-entropy. We solve 3 conjectures on the eccentricity-entropy and give a conjecture on the Wiener-entropy related to some surprising behaviour on the graph minimizing it.
Ključne besede: eccentricity-entropy, Wiener-entropy
Objavljeno v RUP: 21.12.2025; Ogledov: 175; Prenosov: 2
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98. Finding a perfect matching of F_2^n with prescribed differencesBenedek Kovács, 2026, izvirni znanstveni članek Opis: We consider the following question by Balister, Győri and Schelp: given 2^{n-1} nonzero vectors in F_2^n with zero sum, is it always possible to partition the elements of F_2^n into pairs such that the difference between the two elements of the i-th pair is equal to the i-th given vector for every i? An analogous question in F_p, which is a case of the so-called "seating couples" problem, has been resolved by Preissmann and Mischler in 2009. In this paper, we prove the conjecture in F_2^n in the case when the number of distinct values among the given difference vectors is at most n-2log(n)-1, and also in the case when at least a fraction 1/2+ε of the given vectors are equal (for all ε>0 and n sufficiently large based on ε).
Ključne besede: binary vector spaces, seating couples, prescribed differences, perfect matching, functional batch code, graph colourings
Objavljeno v RUP: 21.12.2025; Ogledov: 162; Prenosov: 0
Celotno besedilo (467,06 KB) |
99. Tight toughness variant condition for fractional k-factorsWei Gao, Weifan Wang, Yaojun Chen, 2026, izvirni znanstveni članek Opis: The toughness t(G) of graph G is formalized as the minimum ratio of |S| and ω(G − S) over all vertex subsets S subject to ω(G − S) > 1. As the unique variant parameter of toughness, τ(G) is formulated as the minimum ratio of |S| and ω(G − S) − 1 traversing all the vertex subset S restricted to ω(G − S) ≥ 2. The extant contributions reveal that there is a substantial correlation between toughness and fractional factors. However, there is still a paucity of solid studies on toughness variants τ(G). This work provides several theoretical underpinnings for the tight toughness variant bound for a graph G which admits a fractional k-factor. To be specific, a graph G has a fractional k-factor if τ(G) > k for k ≥ 3 and if τ(G)>3/2 for k = 2. The sharpness of the given bounds is explained by counterexamples.
Ključne besede: graph, toughness, toughness variant, fractional k-factor
Objavljeno v RUP: 21.12.2025; Ogledov: 176; Prenosov: 0
Celotno besedilo (1,11 MB) |
100. Plane triangulations without large 2-treesAllan Bickle, Gunnar Brinkmann, 2026, izvirni znanstveni članek Opis: In 1995 Leizhen Cai asked whether each plane triangulation has a spanning 2-tree. This question was recently answered in the negative by Bickle. He gave a plane triangulation on 38 vertices for which each 2-tree contained in it misses at least one vertex. We give a smaller example on 29 vertices and show that for each c>0 there are plane triangulations P=(V,E), so that each 2-tree that is a subgraph of P contains fewer than c|V| vertices. We also give a lower bound for the size of a maximum 2-tree in plane triangulations by proving that each plane triangulation P=(V,E) contains a 2-tree on at least log_2 (|V|-1)+4 -log_2 3 vertices. Finally we give structural criteria based on the decomposition trees of Jackson and Yu that guarantee the existence of spanning 2-trees in plane triangulations. The results are proven by using the close relation of 2-trees to hamiltonian cycles and to induced trees in the dual for plane triangulations without separating triangles.
Ključne besede: 2-tree, triangulation, Hamiltonian cycle, Yutsis partition
Objavljeno v RUP: 21.12.2025; Ogledov: 152; Prenosov: 1
Celotno besedilo (339,53 KB) |
